Vector coherent state representations, induced representations and geometric quantization

It is shown here and in the preceding paper (Bartlett S D, Rowe D J and Repka J 2002 J. Phys. A: Math. Gen. 35) that vector coherent state theory, the theory of induced representations and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU(3) and rigid rotor models are considered as examples.